Example one: many students don’t know that (of course, assume that . ) Where this came up: when we computed we obtained and a student didn’t understand why this was equal to
I ended up asking the student to simplify and ….asking: ok, “if I have 2/3’rds of a pie and I give two people an equal piece of that, how much pie does each person get?
Example two: I gave “find the domain of and two students didn’t understand why an answer of was logically impossible. One of them told me: “my calculus teacher in high school told me to do it this way”: I am 99.99 percent that this isn’t true, but, well, I stayed with it until the student understood why such a statement was logically impossible. Oh yes, this same “I had calculus in high school” student was sure that I was wrong when I told him that “the derivative of a constant function is zero”; he was SURE that it is “1”.